Measurement of the transverse spatial quantum state of light at the single-photon level: publisher's note.

This publisher's note amends the author listing of Opt. Lett.30, 3365 (2005)OPLEDP0146-959210.1364/OL.30.003365.

Generation of two-temporal-mode photon states by vector four-wave mixing.

Photon pair states and multiple-photon squeezed states have many applications in quantum information science. In this paper, Green functions are derived for spontaneous four-wave mixing in the low- and high-gain regimes. Nondegenerate four-wave mixing in a strongly-birefringent medium generates signal and idler photons that are associated with only one pair of temporal (Schmidt) modes, for a wide range of pump powers and arbitrary pump shapes. The Schmidt coefficients (expected photon numbers) depend sensitively on the pump powers, and the Schmidt functions (shapes of the photon wavepackets) depend sensitively on the pump powers and shapes, which can be controlled.

Temporal mode selectivity by frequency conversion in second-order nonlinear optical waveguides: erratum.

We correct typographical errors in four equations showing the integral forms of the equations of motion and the corresponding perturbative approximation. Subsequently presented derivations, results, and conclusions remain unchanged.

Double-heralded generation of two-photon-states by spontaneous four-wave-mixing in the presence of noise.

We present an experimental method for creating and verifying photon-number states created by non-degenerate, third-order nonlinear-optical photon-pair sources. By using spatially multiplexed, thresholding single-photon detectors and inverting a conditional probability matrix, we determine the photon-number probabilities created through heralded spontaneous four-wave-mixing. The deleterious effects of noise photons on reliable heralding are investigated and shown to degrade the conditional preparation of two-photon number states more than they degrade conditional single-photon states. We derive the equivalence between the presence of unwanted noise in the herald channel and loss in the signal channel of heralded experiments. A procedure for characterizing the noise-photon contributions, and a means of estimating the herald noise-free photon-number distribution is demonstrated.

Temporal mode sorting using dual-stage quantum frequency conversion by asymmetric Bragg scattering.

The temporal shape of single photons provides a high-dimensional basis of temporal modes, and can therefore support quantum computing schemes that go beyond the qubit. However, the lack of linear optical components to act as quantum gates has made it challenging to efficiently address specific temporal-mode components from an arbitrary superposition. Recent progress towards realizing such a "quantum pulse gate," has been proposed using nonlinear optical signal processing to add coherently the effect of multiple stages of quantum frequency conversion. This scheme, called temporal-mode interferometry [D. V. Reddy, Phys. Rev. A 91, 012323 (2015)], has been shown in the case of three-wave mixing to promise near-unity mode-sorting efficiency. Here we demonstrate that it is also possible to achieve high mode-sorting efficiency using four-wave mixing, if one pump pulse is long and the other short - a configuration we call asymmetrically-pumped Bragg scattering.

Efficient sorting of quantum-optical wave packets by temporal-mode interferometry.

Long-distance quantum communication relies on storing and retrieving photonic qubits in orthogonal field modes. The available degrees of freedom for photons are polarization, spatial-mode profile, and temporal/spectral profile. To date, methods exist for decomposing, manipulating, and analyzing photons into orthogonal polarization modes and spatial modes. Here we propose and theoretically verify the first highly efficient method to carry out analogous operations for temporally and spectrally overlapping, but field-orthogonal, temporal modes. The method relies on cascaded nonlinear-optical quantum frequency conversion.

Supercritical xenon-filled hollow-core photonic bandgap fiber.

We demonstrate that filling a hollow-core photonic-bandgap fiber with supercritical xenon creates a medium with a controllable density up to several hundred times that at STP, while working at room temperature. The high compressibility of the supercritical fluid allows rapid tuning of the spectral guidance window by making small changes of gas pressure near the critical point. We discuss potential applications of this system in linear and nonlinear optics.

Temporal mode selectivity by frequency conversion in second-order nonlinear optical waveguides.

We explore theoretically the feasibility of using frequency conversion by sum- or difference-frequency generation, enabled by three-wave-mixing, for selectively multiplexing orthogonal input waveforms that overlap in time and frequency. Such a process would enable a drop device for use in a transparent optical network using temporally orthogonal waveforms to encode different channels. We model the process using coupled-mode equations appropriate for wave mixing in a uniform second-order nonlinear optical medium pumped by a strong laser pulse. We find Green functions describing the process, and employ Schmidt (singular-value) decompositions thereof to quantify its viability in functioning as a coherent waveform discriminator. We define a selectivity figure of merit in terms of the Schmidt coefficients, and use it to compare and contrast various parameter regimes via extensive numerical computations. We identify the most favorable regime (at least in the case of no pump chirp) and derive the complete analytical solution for the same. We bound the maximum achievable selectivity in this parameter space. We show that including a frequency chirp in the pump does not improve selectivity in this optimal regime. We also find an operating regime in which high-efficiency frequency conversion without temporal-shape selectivity can be achieved while preserving the shapes of a wide class of input pulses. The results are applicable to both classical and quantum frequency conversion.

Quantum frequency translation by four-wave mixing in a fiber: low-conversion regime.

In this paper we consider frequency translation enabled by Bragg scattering, a four-wave mixing process. First we introduce the theoretical background of the Green function formalism and the Schmidt decomposition. Next the Green functions for the low-conversion regime are derived perturbatively in the frequency domain, using the methods developed for three-wave mixing, then transformed to the time domain. These results are also derived and verified using an alternative time-domain method, the results of which are more general. For the first time we include the effects of convecting pumps, a more realistic assumption, and show that separability and arbitrary reshaping is possible. This is confirmed numerically for Gaussian pumps as well as higher-order Hermite-Gaussian pumps.

Theory of quantum frequency translation of light in optical fiber: application to interference of two photons of different color.

We study quantum frequency translation and two-color photon interference enabled by the Bragg scattering four-wave mixing process in optical fiber. Using realistic model parameters, we computationally and analytically determine the Green function and Schmidt modes for cases with various pump-pulse lengths. These cases can be categorized as either "non-discriminatory" or "discriminatory" in regards to their propensity to exhibit high-efficiency translation or high-visibility two-photon interference for many different shapes of input wave packets or for only a few input wave packets, respectively. Also, for a particular case, the Schmidt mode set was found to be nearly equal to a Hermite-Gaussian function set. The methods and results also apply with little modification to frequency conversion by sum-frequency conversion in optical crystals.

Remote preparation of complex spatial states of single photons and verification by two-photon coincidence experiment.

We propose and provide experimental evidence in support of a theory for the remote preparation of a complex spatial state of a single photon. An entangled two-photon source was obtained by spontaneous parametric down-conversion, and a double slit was placed in the path of the signal photon as a scattering object. The signal photon was detected after proper spatial filtering so that the idler photon was prepared in the corresponding single-photon state. By using a two-photon coincidence measurement, we obtained the Radon transform, at several longitudinal distances, of the single-photon Wigner distribution function modified by the double slit. The experimental results are consistent with the idler photon being in a pure state. An inverse Radon transformation can, in principle, be applied to the measured data to reconstruct the modified single-photon Wigner function, which is a complete representation of the amplitude and phase structure of the scattering object.

Quantum-fluctuation-initiated coherence in multioctave Raman optical frequency combs.

We show experimentally and theoretically that the spectral components of a multioctave frequency comb spontaneously created by stimulated Raman scattering in a hydrogen-filled hollow-core photonic crystal fiber exhibit strong self-coherence and mutual coherence within each 12 ns driving laser pulse. This coherence arises in spite of the field's initiation being from quantum zero-point fluctuations, which causes each spectral component to show large phase and energy fluctuations. This points to the possibility of an optical frequency comb with nonclassical correlations between all comb lines.

Quantum frequency translation of single-photon states in a photonic crystal fiber.

We experimentally demonstrate frequency translation of a nonclassical optical field via four-wave mixing (Bragg-scattering process) in a photonic crystal fiber (PCF). The high nonlinearity and the ability to control dispersion in PCF enable efficient translation between nearby photon channels within the visible to-near-infrared spectral range, useful in quantum networks. Heralded single photons at 683 nm were translated to 659 nm with an efficiency of 28.6±2.2 percent. Second-order correlation measurements on the 683- and 659-nm fields yielded g(683)(2) (0)=0.21±0.02 and g(659)(2) (0)=0.19±0.05, respectively, showing the nonclassical nature of both fields.

Stable mode sorting by two-dimensional parity of photonic transverse spatial states.

We describe a mode sorter for two-dimensional parity of transverse spatial states of light based on an out-of-plane Sagnac interferometer. Both Hermite-Gauss (HG) and Laguerre-Gauss (LG) modes can be guided into one of two output ports according to the two-dimensional parity of the mode in question. Our interferometer sorts HG(nm) input modes depending upon whether they have even or odd order n+m; it equivalently sorts LG(l)(p) modes depending upon whether they have an even or odd value of their orbital angular momentum l. It functions efficiently at the single-photon level, and therefore can be used to sort single-photon states. Due to the inherent phase stability of this type of interferometer as compared to those of the Mach-Zehnder type, it provides a promising tool for the manipulation and filtering of higher order transverse spatial modes for the purposes of quantum information processing. For example, several similar Sagnacs cascaded together may allow, for the first time, a stable measurement of the orbital angular momentum of a true single-photon state. Furthermore, as an alternative to well-known holographic techniques, one can use the Sagnac in conjunction with a multi-mode fiber as a spatial mode filter, which can be used to produce spatial-mode entangled Bell states and heralded single photons in arbitrary first-order (n+m = 1) spatial states, covering the entire Poincar e sphere of first-order transverse modes.

Multicolor multipartite entanglement produced by vector four-wave mixing in a fiber.

Multipartite entanglement is a resource for quantum communication and computation. Vector four-wave mixing (FWM) in a fiber, driven by two strong optical pumps, couples the evolution of four weak optical sidebands (modes). Depending on the fiber dispersion and pump frequencies, the mode frequencies can be similar (separated by less than 1 THz) or dissimilar (separated by more than 10 THz). In this report, the discrete- and continuous-variable entanglement produced by vector FWM is studied in detail. Formulas are derived for the variances of, and correlations between, the mode quadratures and photon numbers. These formulas and related results show that the modes are four-partite entangled.

Unimpaired phase-sensitive amplification by vector four-wave mixing near the zero-dispersion frequency.

Phase-sensitive amplification (PSA), which is produced by degenerate four-wave mixing (FWM) in a randomly-birefringent fiber, has the potential to improve the performance of optical communication systems. Scalar FWM, which is driven by parallel pumps, is impaired by the generation of pump-pump and pump-signal harmonics, which limit the level, and modify the phase sensitivity, of the signal gain. In contrast, vector FWM, which is driven by perpendicular pumps, is not impaired by the generation of harmonics. Vector FWM produces PSA with the classical properties of a one-mode squeezing transformation.

Photon pair-state preparation with tailored spectral properties by spontaneous four-wave mixing in photonic-crystal fiber.

We study theoretically the generation of photon pairs by spontaneous four-wave mixing (SFWM) in photonic crystal optical fiber. We show that it is possible to engineer two-photon states with specific spectral correlation ("entanglement") properties suitable for quantum information processing applications. We focus on the case exhibiting no spectral correlations in the two-photon component of the state, which we call factorability, and which allows heralding of single-photon pure-state wave packets without the need for spectral post filtering. We show that spontaneous four wave mixing exhibits a remarkable flexibility, permitting a wider class of two-photon states, including ultra-broadband, highly-anticorrelated states.

A hemispherical, high-solid-angle optical micro-cavity for cavity-QED studies.

We report a novel hemispherical micro-cavity that is comprised of a planar integrated semiconductor distributed Bragg reflector (DBR) mirror, and an external, concave micro-mirror having a radius of curvature 50 microm. The integrated DBR mirror containing quantum dots (QD), is designed to locate the QDs at an antinode of the field in order to maximize the interaction between the QD and cavity. The concave micro-mirror, with high-reflectivity over a large solid-angle, creates a diffraction-limited (sub-micron) mode-waist at the planar mirror, leading to a large coupling constant between the cavity mode and QD. The half-monolithic design gives more spatial and spectral tuning abilities, relatively to fully monolithic structures. This unique micro-cavity design will potentially enable us to both reach the cavity quantum electrodynamics (QED) strong coupling regime and realize the deterministic generation of single photons on demand.

Quantum noise properties of parametric processes.

In this paper the quantum noise properties of phase-insensitive and phase-sensitive parametric processes are studied. Formulas for the field-quadrature and photon-number means and variances are derived, for processes that involve arbitrary numbers of modes. These quantities determine the signal-to-noise ratios associated with the direct and homo-dyne detection of optical signals. The consequences of the aforementioned formulas are described for frequency conversion, amplification, monitoring, and transmission through sequences of attenuators and amplifiers.

Entangled photon-pair two-dimensional fluorescence spectroscopy (EPP-2DFS).

We introduce a new method, called entangled photon-pair two-dimensional fluorescence spectroscopy (EPP-2DFS), to sensitively probe the nonlinear electronic response of molecular systems. The method incorporates a separated two-photon ('Franson') interferometer, which generates time-frequency-entangled photon pairs, into the framework of a fluorescence-detected 2D optical spectroscopic experiment. The entangled photons are temporally shaped and phase-modulated in the interferometer, and are used to excite a two-photon-absorbing (TPA) sample, whose excited-state population is selectively detected by simultaneously monitoring the sample fluorescence and the exciting fields. In comparison to 'classical' 2DFS techniques, major advantages of this scheme are the suppression of uncorrelated background signals, the enhancement of simultaneous time-and-frequency resolution, the suppression of diagonal 2D spectral features, and the enhancement and narrowing of off-diagonal spectral cross-peaks that contain information about electronic couplings. These effects are a consequence of the pure-state field properties unique to a parametric down-conversion light source, which must be included in the quantum mechanical description of the composite field-molecule system. We numerically simulate the EPP-2DFS observable for the case of an electronically coupled molecular dimer. The EPP-2DFS spectrum is greatly simplified in comparison to its classical 2D counterpart. Our results indicate that EPP-2DFS can provide previously unattainable resolution to extract model Hamiltonian parameters from electronically coupled molecular dimers.